NSLS Activity Report 2006 - Brookhaven National Laboratory

energy gap, responsible for suppressing quantum
fluctuations.
What is the source of the energy gap? And here is
a related question: What makes the spins prefer
the a-b plane instead of making a helical structure
in some different planes? The anisotropy in interaction
between the spins is needed to answer both
of these questions. In this case the anisotropy is
of the “easy plane” type: The interaction energies
are larger for spins in the a-b plane than for spins
in other directions. We performed theoretical modeling
and, by fitting the resonance positions for all
field, we determined a single anisotropy parameter
for this system. The model also described the
observed strong field dependence in the intensity
of the resonance.
Figure 1. Crystal structure of LiCu 2 O 2 . The magnetic Cu 2+
ions are dark blue, the non-magnetic copper is green, the
lithium is light blue and the oxygen is red. The dark blue
bonds emphasize the triangular spin ladder.
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Interestingly, the model predicted two resonances
at finite fields, but the other one (green line in
Figure 3) was much weaker. We suspected that
the instrument we used was not sensitive enough
to see this other line, and we sent the sample
back to EPFL, (Lausanne, Switzerland), where
Bálint Náfrádi did more ESR measurements. The
spectrometer in Lausanne operates at a few fixed
frequencies, and it cannot be used to create a full
two-dimensional map of absorption intensity seen
in Figure 3, but it is much more sensitive than
ours. The resonance line has been found at the
predicted position, and we witnessed one of the
rare cases when the theory not only interpreted
the existing experimental data, but actually predicted
the result of a new experiment.
Figure 2. Helical spin order along a triangular ladder in
LiCu 2 O 2 . All spin directions are parallel to the a-b plane,
and subsequent spins on the same leg of the ladder make
an angle slightly larger than 60 o .
Figure 3. Upper panel: Absorption due to spin resonance
as a function of fi eld and frequency. Darker shades indicate
stronger absorption. The red line is a theoretical fi t to the
line position. The green line is another resonance predicted
by the theory. Lower panel: Simulated experimental results,
based on the calculated intensity of the absorption.
CONDENSED MATTER PHYSICS